Strong Coupling Topological Phases in Moiré Bands

Abstract

A central goal of quantum condensed matter physics is to understand, realize, and control phases of matter that exhibit macroscopic quantum phenomena. Moiré materials offer an unprecedented ability to do so through hosting strongly interacting electrons in topological bands. This setting was previously restricted to the FQHE, where electrons under massive magnetic fields split into new particles that carry a fraction of the electron's charge. This newly central experimental setting demands new theoretical tools that are applicable to strongly interacting topological bands. Existing theories are, naturally, specific to the only prior existing example, the lowest Landau level associated with the traditional fractional quantum Hall effect, and by their nature rule out several phases of matter including superconductivity. In this thesis, we develop strong coupling theories in the topological setting and use them make predictions on the interacting physics of twisted graphene systems. In Chapter 1, we will show how to analytically predict fractionalization in topological bands without relying on mimicking the lowest Landau level. Chapter 2 will compare and contrast a class of twisted graphene systems using a variety of theoretical tools. In Chapter 3, we report on a theoretical framework that accesses Mott physics in the topological bands of TBG. Mott physics, a key ingredient of high temperature superconductors, is typically studied in bands without topology. We report on qualitatively new phenomena that emerge from the combination of Mott physics and band topology.